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Simplifying x2 + 19x + 9 = 0 Reorder the terms: 9 + 19x + x2 = 0 Solving 9 + 19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-9' to each side of the equation. 9 + 19x + -9 + x2 = 0 + -9 Reorder the terms: 9 + -9 + 19x + x2 = 0 + -9 Combine like terms: 9 + -9 = 0 0 + 19x + x2 = 0 + -9 19x + x2 = 0 + -9 Combine like terms: 0 + -9 = -9 19x + x2 = -9 The x term is 19x. Take half its coefficient (9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. 19x + 90.25 + x2 = -9 + 90.25 Reorder the terms: 90.25 + 19x + x2 = -9 + 90.25 Combine like terms: -9 + 90.25 = 81.25 90.25 + 19x + x2 = 81.25 Factor a perfect square on the left side: (x + 9.5)(x + 9.5) = 81.25 Calculate the square root of the right side: 9.013878189 Break this problem into two subproblems by setting (x + 9.5) equal to 9.013878189 and -9.013878189.Subproblem 1
x + 9.5 = 9.013878189 Simplifying x + 9.5 = 9.013878189 Reorder the terms: 9.5 + x = 9.013878189 Solving 9.5 + x = 9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = 9.013878189 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = 9.013878189 + -9.5 x = 9.013878189 + -9.5 Combine like terms: 9.013878189 + -9.5 = -0.486121811 x = -0.486121811 Simplifying x = -0.486121811Subproblem 2
x + 9.5 = -9.013878189 Simplifying x + 9.5 = -9.013878189 Reorder the terms: 9.5 + x = -9.013878189 Solving 9.5 + x = -9.013878189 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-9.5' to each side of the equation. 9.5 + -9.5 + x = -9.013878189 + -9.5 Combine like terms: 9.5 + -9.5 = 0.0 0.0 + x = -9.013878189 + -9.5 x = -9.013878189 + -9.5 Combine like terms: -9.013878189 + -9.5 = -18.513878189 x = -18.513878189 Simplifying x = -18.513878189Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.486121811, -18.513878189}
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